Second-order photonic topological insulators that host highly localized corner states resilient to defects, are opening new routes towards developing fascinating devices. However, the existing works on second-order have mainly focused either transverse magnetic or electric modes. In this paper, we propose a dual-polarization crystal structure for both and modes through topology optimization. Si...

This paper provides a new formulation of second order stochastic target problems introduced in [19] by modifying the reference probability so as to allow for different scales. This new ingredient enables us to prove a dual formulation of the target problem as the supremum of the solutions of standard backward stochastic differential equations. In particular, in the Markov case, the dual problem...

A power assignment is an assignment of transmission power to each of the wireless nodes of a wireless network, so that the induced graph satisfies some desired properties. The cost of a power assignment is the sum of the assigned powers. In this paper, we consider the dual power assignment problem, in which each wireless node is assigned a highor low-power level, so that the induced graph is st...